What separates a vector quantity from a scalar quantity?

A vector has magnitude and direction; a scalar has magnitude only. Velocity is a vector, while speed is a scalar.

When is the point-object model useful in kinematics?

When an object's size and rotation do not matter for the motion being studied. Its position can then represent the whole object.

When may the constant-acceleration kinematic equations be used?

Only over an interval with constant acceleration. They are not general formulas for changing acceleration.

Why must a velocity statement name or imply a reference frame?

Velocity depends on the observer's frame. The same object can be at rest in one frame and moving in another.

Why can horizontal and vertical projectile motion be analyzed separately?

Perpendicular components evolve independently. With negligible air resistance, gravity changes only the vertical component.

Can an object have zero velocity and nonzero acceleration at one instant?

Yes. At the top of a vertical toss, velocity is momentarily zero while gravitational acceleration still points downward.

A runner completes one lap and returns to the start. How do distance and displacement compare?

The distance is one lap, while the displacement is zero. Displacement depends only on the change from initial to final position.

What makes a reference frame convenient for a motion problem?

It makes the relevant positions or velocities simple. A good frame reduces bookkeeping without changing physical predictions.

How are the components of a launch velocity v at angle θ found?

v_x = v cos θ and v_y = v sin θ. The angle is measured from the positive horizontal axis.

What does average velocity measure?

Displacement per elapsed time. In one dimension, v_avg = Δx/Δt; direction comes from the sign of Δx.

Do a vector's magnitude and its component use different SI units?

No. A vector and each of its components use the same unit; for example, velocity and its x-component both use m/s.

A velocity-versus-time graph curves upward and becomes progressively steeper while staying above zero. What does that show?

The object moves in the positive direction and speeds up with increasing positive acceleration. The graph's slope is acceleration; because that slope changes, the acceleration is nonuniform.

What are a projectile's horizontal and vertical accelerations when air resistance is negligible and up is positive?

a_x = 0 and a_y = -g. Horizontal velocity stays constant while vertical velocity changes.

What does average acceleration measure?

Change in velocity per elapsed time. In one dimension, a_avg = Δv/Δt.

What does a negative one-dimensional vector component mean?

It points opposite the chosen positive direction. The minus sign describes direction, not a negative physical size.

For constant acceleration, what does v = v₀ + at retrieve?

Velocity after elapsed time t. Use it when initial velocity, constant acceleration, and time are known or related.

How are a vector's magnitude and direction reconstructed from perpendicular components v_x and v_y?

v = √(v_x² + v_y²). When v_x ≠ 0, use θ = tan⁻¹(v_y/v_x) and the component signs to choose the quadrant. If v_x = 0 and v_y ≠ 0, the vector points along +y or -y; if both components are zero, its direction is undefined.

At an instant when velocity is nonzero, how do velocity and acceleration signs show whether a one-dimensional object is speeding up?

It speeds up when velocity and acceleration have the same sign. Opposite signs mean speed is decreasing at that instant.

What does the slope of a position-versus-time graph represent?

Velocity. A steeper slope means a larger speed, and the slope's sign gives direction.

Two observers use inertial frames, where an object with zero net force has constant velocity. If the observers move at constant velocity relative to each other, do they agree on an object's acceleration?

Yes, in a Galilean inertial-frame model. Subtracting a constant frame velocity changes velocity but not acceleration. This definition distinguishes an inertial frame from an accelerating, noninertial frame.

A projectile lands at its launch height with negligible air resistance. How do its launch and landing speeds compare?

They are equal. The horizontal component is unchanged, and the vertical component returns with equal magnitude and opposite sign.

A car's velocity changes from -2 m/s to +6 m/s in 2 s. What is its average acceleration?

+4 m/s². Δv = 8 m/s, and 8 m/s ÷ 2 s = 4 m/s².

If the positive axis is reversed, what happens to a one-dimensional vector component and its magnitude?

The component changes sign, while the magnitude stays the same. A coordinate choice changes the signed description, not the physical vector.

For constant acceleration, what does Δx = v₀t + ½at² retrieve?

Displacement over time t. It includes both initial-velocity motion and the displacement added by constant acceleration.

For a horizontal launch from height h in uniform gravity with negligible air resistance, what sets the time to reach the ground?

The vertical drop alone. Starting with v_y = 0, the time follows h = ½gt² and does not depend on horizontal speed.

Why can average speed differ from the magnitude of average velocity?

Average speed uses total distance, while average velocity uses displacement. Reversing direction increases distance without necessarily increasing displacement.

What does the slope of a velocity-versus-time graph represent?

Acceleration. The slope's units are (m/s)/s = m/s².

A passenger walks forward at 2 m/s inside a train moving forward at 18 m/s. What is the passenger's ground velocity?

20 m/s forward. Add the passenger's train-relative velocity to the train's ground velocity.

Does projectile mass affect the ideal trajectory when air resistance is negligible?

No. All projectiles have the same gravitational acceleration, so equal initial conditions give equal trajectories.

Can an object have nonzero velocity and zero acceleration?

Yes. Constant-velocity motion has nonzero velocity while the velocity change, and therefore acceleration, is zero.

A cart starts from rest with constant acceleration. Which graph should be linear if x = x₀ + ½at² applies?

Position x versus t². Its slope is ½a when the initial velocity is zero.

What does signed area under a velocity-versus-time graph represent?

Displacement. Area below the time axis contributes negative displacement.

At the highest point of a projectile's path, what are its vertical velocity and vertical acceleration?

v_y = 0, but a_y = -g. The vertical velocity pauses before reversing; gravity does not switch off.

How can a motion sensor test whether a cart moves at constant velocity?

Record position at equal time intervals and graph position versus time. A straight line with nearly constant slope supports constant velocity.

A car passes a parked observer at 12 m/s. What is the parked observer's velocity in the car's frame?

-12 m/s. In the car's frame, the ground and observer move backward at the car's speed.

Which constant-acceleration equation connects speed and displacement without using time?

v² = v₀² + 2aΔx. Use signed one-dimensional quantities and constant acceleration.

How could video data test the independence of projectile components?

Track x and y at equal times. A linear x-versus-t graph and a quadratic vertical trend support constant horizontal velocity and vertical acceleration.

A velocity-versus-time graph stays below zero but slopes upward toward zero. What is happening?

The object moves in the negative direction while slowing down. Velocity is negative and acceleration is positive.

How can average velocity over a very short interval approximate instantaneous velocity?

Shrink the time interval around the instant. The displacement divided by that short interval approaches the local position–time graph slope.

A walker moves 7 m east, then 3 m west. What is the one-dimensional displacement if east is positive?

+4 m. Add signed displacements: +7 m + (-3 m) = +4 m.

What shape is the path of a projectile with a nonzero horizontal velocity component in a uniform gravitational field when air resistance is negligible?

A parabola. Constant horizontal velocity and constant vertical acceleration produce the curve. A purely vertical launch is the special case: its spatial path is a vertical line.

In a motion diagram with dots at equal time intervals and velocity arrows, what do wider dot spacing and longer arrows show?

Greater speed. Wider spacing means more distance is covered during each equal time interval, while longer velocity arrows represent a larger velocity magnitude. Each arrow points in the direction of motion.

What does signed area under an acceleration-versus-time graph represent?

Change in velocity. Add that signed area to the initial velocity to find the final velocity.

How is one-dimensional relative velocity calculated for two objects A and B?

v_A relative to B = v_A - v_B. Both velocities must be measured in the same frame before subtracting.

When its speed is nonzero, what direction does a projectile's instantaneous velocity point?

Tangent to its path. Its horizontal and vertical velocity components combine to set that direction.

What does choosing a system boundary decide in a mechanics problem?

It decides which objects belong to the system and which forces count as external. Internal interactions occur between objects inside the boundary.

What belongs on a free-body diagram for one chosen object?

Only forces exerted on that object by other objects. Do not draw velocity, acceleration, or forces the chosen object exerts elsewhere.

What assumptions define the ideal-string model used in introductory algebra-based physics?

The string is massless, inextensible, and flexible. It pulls along its length, doesn't stretch, and can redirect around an ideal pulley.

What does translational equilibrium require?

Zero net force. The object may be at rest or move with constant velocity.

In an inertial frame, how does Newton's second law connect force and motion?

ΣF = ma. The net external force on the chosen object or system causes its acceleration; mass sets how strongly the velocity responds.

How do mass and weight differ?

Mass measures inertia in kilograms; weight is gravitational force in newtons. Near a surface, F_g = mg.

AP Physics 1 Flashcards: Complete 8-Unit Course Review

A 400-card AP Physics 1 review of concepts, formulas, graphs, experiments, and reasoning across all eight course units.

Автор Open Study Contributor

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Данни за тестето

Карти: 400 карти
Версия: 3
Публикувано: 26 август 2026 г.
Последна актуализация: 10 септември 2026 г.
Лиценз: Common knowledge · CC0 1.0
Езици на аудиторията: en
Предмет: Physics
Ниво: AP Physics 1
Етикети: algebra-based-physics-1, unit-1, unit-2, unit-3, unit-4, unit-5, unit-6, unit-7, unit-8

Подобни тестета

За това тесте

This 400-card deck reviews all eight AP Physics 1 course units: Kinematics; Force and Translational Dynamics; Work, Energy, and Power; Linear Momentum; Torque and Rotational Dynamics; Energy and Momentum of Rotating Systems; Oscillations; and Fluids.

What you'll retrieve

Choose the governing principle for a situation or claim, then explain the prediction in plain language.
Recall what a quantity or equation means, when it applies, how it scales, and which SI unit it uses.
Read slopes, signed areas, extrema, signs, and shapes across motion, force, energy, momentum, rotation, oscillation, and fluid graphs.
Plan a small experiment by naming useful variables, measurements, controls, linearized graphs, slope meanings, and uncertainty checks.
Solve one focused original algebra-based setup with units and a short reason.
Use selected reverse and contrast prompts to recognize conditions and separate common confusion pairs.

The deck does not mechanically reverse every fact. Bare formula-to-symbol lists, long multipart calculations, and imitation exam questions are excluded.

The sequence follows Units 1–8 so motion, forces, energy, and momentum become prerequisites for rotation, orbits, oscillations, and fluids. Definitions appear before dependent uses, while related formula, graph, condition, calculation, and contrast prompts are separated where practical to reduce short-range cueing.

Course scope was checked against the official AP Physics 1 course page. Every prompt, answer, numerical setup, explanation, ordering choice, and metadata field was independently written from common physics knowledge. The CC0 label applies to that original expression and organization to the extent applicable rights exist; it does not claim ownership of physics facts or third-party material.

This is an independently authored, unofficial educational deck. It is not affiliated with, sponsored by, or endorsed by the College Board. AP® is a trademark registered by the College Board, which is not affiliated with, and does not endorse, this product. No AP exam questions, answer keys, scoring guidelines, curriculum text, logos, or trade dress were copied.

Карти в това тесте

Карта 1
Въпрос
What separates a vector quantity from a scalar quantity?
Отговор
A vector has magnitude and direction; a scalar has magnitude only. Velocity is a vector, while speed is a scalar.
Карта 2
Въпрос
When is the point-object model useful in kinematics?
Отговор
When an object's size and rotation do not matter for the motion being studied. Its position can then represent the whole object.
Карта 3
Въпрос
When may the constant-acceleration kinematic equations be used?
Отговор
Only over an interval with constant acceleration. They are not general formulas for changing acceleration.
Карта 4
Въпрос
Why must a velocity statement name or imply a reference frame?
Отговор
Velocity depends on the observer's frame. The same object can be at rest in one frame and moving in another.
Карта 5
Въпрос
Why can horizontal and vertical projectile motion be analyzed separately?
Отговор
Perpendicular components evolve independently. With negligible air resistance, gravity changes only the vertical component.
Карта 6
Въпрос
Can an object have zero velocity and nonzero acceleration at one instant?
Отговор
Yes. At the top of a vertical toss, velocity is momentarily zero while gravitational acceleration still points downward.
Карта 7
Въпрос
A runner completes one lap and returns to the start. How do distance and displacement compare?
Отговор
The distance is one lap, while the displacement is zero. Displacement depends only on the change from initial to final position.
Карта 8
Въпрос
What makes a reference frame convenient for a motion problem?
Отговор
It makes the relevant positions or velocities simple. A good frame reduces bookkeeping without changing physical predictions.
Карта 9
Въпрос
How are the components of a launch velocity v at angle θ found?
Отговор
v_x = v cos θ and v_y = v sin θ. The angle is measured from the positive horizontal axis.
Карта 10
Въпрос
What does average velocity measure?
Отговор
Displacement per elapsed time. In one dimension, v_avg = Δx/Δt; direction comes from the sign of Δx.
Карта 11
Въпрос
Do a vector's magnitude and its component use different SI units?
Отговор
No. A vector and each of its components use the same unit; for example, velocity and its x-component both use m/s.
Карта 12
Въпрос
A velocity-versus-time graph curves upward and becomes progressively steeper while staying above zero. What does that show?
Отговор
The object moves in the positive direction and speeds up with increasing positive acceleration. The graph's slope is acceleration; because that slope changes, the acceleration is nonuniform.
Карта 13
Въпрос
What are a projectile's horizontal and vertical accelerations when air resistance is negligible and up is positive?
Отговор
a_x = 0 and a_y = -g. Horizontal velocity stays constant while vertical velocity changes.
Карта 14
Въпрос
What does average acceleration measure?
Отговор
Change in velocity per elapsed time. In one dimension, a_avg = Δv/Δt.
Карта 15
Въпрос
What does a negative one-dimensional vector component mean?
Отговор
It points opposite the chosen positive direction. The minus sign describes direction, not a negative physical size.
Карта 16
Въпрос
For constant acceleration, what does v = v₀ + at retrieve?
Отговор
Velocity after elapsed time t. Use it when initial velocity, constant acceleration, and time are known or related.
Карта 17
Въпрос
How are a vector's magnitude and direction reconstructed from perpendicular components v_x and v_y?
Отговор
v = √(v_x² + v_y²). When v_x ≠ 0, use θ = tan⁻¹(v_y/v_x) and the component signs to choose the quadrant. If v_x = 0 and v_y ≠ 0, the vector points along +y or -y; if both components are zero, its direction is undefined.
Карта 18
Въпрос
At an instant when velocity is nonzero, how do velocity and acceleration signs show whether a one-dimensional object is speeding up?
Отговор
It speeds up when velocity and acceleration have the same sign. Opposite signs mean speed is decreasing at that instant.
Карта 19
Въпрос
What does the slope of a position-versus-time graph represent?
Отговор
Velocity. A steeper slope means a larger speed, and the slope's sign gives direction.
Карта 20
Въпрос
Two observers use inertial frames, where an object with zero net force has constant velocity. If the observers move at constant velocity relative to each other, do they agree on an object's acceleration?
Отговор
Yes, in a Galilean inertial-frame model. Subtracting a constant frame velocity changes velocity but not acceleration. This definition distinguishes an inertial frame from an accelerating, noninertial frame.
Карта 21
Въпрос
A projectile lands at its launch height with negligible air resistance. How do its launch and landing speeds compare?
Отговор
They are equal. The horizontal component is unchanged, and the vertical component returns with equal magnitude and opposite sign.
Карта 22
Въпрос
A car's velocity changes from -2 m/s to +6 m/s in 2 s. What is its average acceleration?
Отговор
+4 m/s². Δv = 8 m/s, and 8 m/s ÷ 2 s = 4 m/s².
Карта 23
Въпрос
If the positive axis is reversed, what happens to a one-dimensional vector component and its magnitude?
Отговор
The component changes sign, while the magnitude stays the same. A coordinate choice changes the signed description, not the physical vector.
Карта 24
Въпрос
For constant acceleration, what does Δx = v₀t + ½at² retrieve?
Отговор
Displacement over time t. It includes both initial-velocity motion and the displacement added by constant acceleration.
Карта 25
Въпрос
For a horizontal launch from height h in uniform gravity with negligible air resistance, what sets the time to reach the ground?
Отговор
The vertical drop alone. Starting with v_y = 0, the time follows h = ½gt² and does not depend on horizontal speed.
Карта 26
Въпрос
Why can average speed differ from the magnitude of average velocity?
Отговор
Average speed uses total distance, while average velocity uses displacement. Reversing direction increases distance without necessarily increasing displacement.
Карта 27
Въпрос
What does the slope of a velocity-versus-time graph represent?
Отговор
Acceleration. The slope's units are (m/s)/s = m/s².
Карта 28
Въпрос
A passenger walks forward at 2 m/s inside a train moving forward at 18 m/s. What is the passenger's ground velocity?
Отговор
20 m/s forward. Add the passenger's train-relative velocity to the train's ground velocity.
Карта 29
Въпрос
Does projectile mass affect the ideal trajectory when air resistance is negligible?
Отговор
No. All projectiles have the same gravitational acceleration, so equal initial conditions give equal trajectories.
Карта 30
Въпрос
Can an object have nonzero velocity and zero acceleration?
Отговор
Yes. Constant-velocity motion has nonzero velocity while the velocity change, and therefore acceleration, is zero.
Карта 31
Въпрос
A cart starts from rest with constant acceleration. Which graph should be linear if x = x₀ + ½at² applies?
Отговор
Position x versus t². Its slope is ½a when the initial velocity is zero.
Карта 32
Въпрос
What does signed area under a velocity-versus-time graph represent?
Отговор
Displacement. Area below the time axis contributes negative displacement.
Карта 33
Въпрос
At the highest point of a projectile's path, what are its vertical velocity and vertical acceleration?
Отговор
v_y = 0, but a_y = -g. The vertical velocity pauses before reversing; gravity does not switch off.
Карта 34
Въпрос
How can a motion sensor test whether a cart moves at constant velocity?
Отговор
Record position at equal time intervals and graph position versus time. A straight line with nearly constant slope supports constant velocity.
Карта 35
Въпрос
A car passes a parked observer at 12 m/s. What is the parked observer's velocity in the car's frame?
Отговор
-12 m/s. In the car's frame, the ground and observer move backward at the car's speed.
Карта 36
Въпрос
Which constant-acceleration equation connects speed and displacement without using time?
Отговор
v² = v₀² + 2aΔx. Use signed one-dimensional quantities and constant acceleration.
Карта 37
Въпрос
How could video data test the independence of projectile components?
Отговор
Track x and y at equal times. A linear x-versus-t graph and a quadratic vertical trend support constant horizontal velocity and vertical acceleration.
Карта 38
Въпрос
A velocity-versus-time graph stays below zero but slopes upward toward zero. What is happening?
Отговор
The object moves in the negative direction while slowing down. Velocity is negative and acceleration is positive.
Карта 39
Въпрос
How can average velocity over a very short interval approximate instantaneous velocity?
Отговор
Shrink the time interval around the instant. The displacement divided by that short interval approaches the local position–time graph slope.
Карта 40
Въпрос
A walker moves 7 m east, then 3 m west. What is the one-dimensional displacement if east is positive?
Отговор
+4 m. Add signed displacements: +7 m + (-3 m) = +4 m.
Карта 41
Въпрос
What shape is the path of a projectile with a nonzero horizontal velocity component in a uniform gravitational field when air resistance is negligible?
Отговор
A parabola. Constant horizontal velocity and constant vertical acceleration produce the curve. A purely vertical launch is the special case: its spatial path is a vertical line.
Карта 42
Въпрос
In a motion diagram with dots at equal time intervals and velocity arrows, what do wider dot spacing and longer arrows show?
Отговор
Greater speed. Wider spacing means more distance is covered during each equal time interval, while longer velocity arrows represent a larger velocity magnitude. Each arrow points in the direction of motion.
Карта 43
Въпрос
What does signed area under an acceleration-versus-time graph represent?
Отговор
Change in velocity. Add that signed area to the initial velocity to find the final velocity.
Карта 44
Въпрос
How is one-dimensional relative velocity calculated for two objects A and B?
Отговор
v_A relative to B = v_A - v_B. Both velocities must be measured in the same frame before subtracting.
Карта 45
Въпрос
When its speed is nonzero, what direction does a projectile's instantaneous velocity point?
Отговор
Tangent to its path. Its horizontal and vertical velocity components combine to set that direction.
Карта 46
Въпрос
What does choosing a system boundary decide in a mechanics problem?
Отговор
It decides which objects belong to the system and which forces count as external. Internal interactions occur between objects inside the boundary.
Карта 47
Въпрос
What belongs on a free-body diagram for one chosen object?
Отговор
Only forces exerted on that object by other objects. Do not draw velocity, acceleration, or forces the chosen object exerts elsewhere.
Карта 48
Въпрос
What assumptions define the ideal-string model used in introductory algebra-based physics?
Отговор
The string is massless, inextensible, and flexible. It pulls along its length, doesn't stretch, and can redirect around an ideal pulley.
Карта 49
Въпрос
What does translational equilibrium require?
Отговор
Zero net force. The object may be at rest or move with constant velocity.
Карта 50
Въпрос
In an inertial frame, how does Newton's second law connect force and motion?
Отговор
ΣF = ma. The net external force on the chosen object or system causes its acceleration; mass sets how strongly the velocity responds.
Карта 51
Въпрос
How do mass and weight differ?
Отговор
Mass measures inertia in kilograms; weight is gravitational force in newtons. Near a surface, F_g = mg.
Карта 52
Въпрос
How does static friction choose its magnitude before slipping begins?
Отговор
It matches the needed tangential contact force up to a maximum. In general, f_s ≤ μ_sN.
Карта 53
Въпрос
For an ideal spring in its linear range, what is the spring force when its end is displaced by a signed amount x from the relaxed or natural length?
Отговор
F_s = -kx. The sign shows that the spring force opposes the signed extension or compression and points toward the relaxed or natural length.
Карта 54
Въпрос
What direction does centripetal acceleration point in circular motion?
Отговор
Toward the circle's center. It changes the velocity's direction even when speed is constant.
Карта 55
Въпрос
What is the gravitational force magnitude between two point masses?
Отговор
F_g = Gm₁m₂/r². Here r is the center-to-center separation.
Карта 56
Въпрос
Why isn't the normal force always equal to an object's weight?
Отговор
It adjusts to the contact and acceleration conditions. Other vertical forces or vertical acceleration can change its magnitude.
Карта 57
Въпрос
What determines a friction coefficient in the simple model?
Отговор
The pair of contacting materials and their surface condition. It isn't a universal property of either material alone.
Карта 58
Въпрос
What is the centripetal-acceleration magnitude for speed v and radius r?
Отговор
a_c = v²/r. It is a kinematic requirement, not a separate force.
Карта 59
Въпрос
An elevator accelerates upward. How does the scale reading compare with a rider's weight?
Отговор
It is greater than the weight. Upward net force requires N - mg > 0.
Карта 60
Въпрос
What does a spring constant k measure, and what is its SI unit?
Отговор
It measures stiffness in N/m. A larger k means more force is needed for the same displacement in the linear range.
Карта 61
Въпрос
Three equal point masses are at (0,0), (3 m,0), and (0,3 m). Where is their center of mass?
Отговор
At (1 m,1 m). Average the x-coordinates and y-coordinates separately for equal masses.
Карта 62
Въпрос
What provides centripetal force?
Отговор
The inward component of real forces such as tension, gravity, friction, or a normal force. 'Centripetal force' names their net inward result.
Карта 63
Въпрос
How is near-surface gravitational field strength related to weight?
Отговор
F_g = mg. The local field strength g has units N/kg, equivalent to m/s².
Карта 64
Въпрос
How is weight resolved on an incline of angle θ measured from horizontal?
Отговор
mg sin θ points down the slope and mg cos θ points into the slope. These are components of one gravitational force.
Карта 65
Въпрос
What does Newton's third law say about an interaction between objects A and B?
Отговор
The force of A on B and the force of B on A have equal magnitude and opposite direction. They act on different objects.
Карта 66
Въпрос
What does signed tangential acceleration describe during circular motion?
Отговор
It describes how quickly speed changes and which way the tangential acceleration points along the chosen tangent. Its magnitude is the absolute value of the instantaneous rate of change of speed. If it points with the velocity, speed increases; if it points against the velocity, speed decreases. Its sign follows the chosen tangent.
Карта 67
Въпрос
What happens to gravitational force if the separation between two point masses doubles?
Отговор
It becomes one-fourth as large. The force follows an inverse-square dependence on distance.
Карта 68
Въпрос
How can an adjustable incline estimate a block's coefficient of static friction when no other applied force acts?
Отговор
Raise the incline slowly until the block just begins to slide. At that threshold, the simple block model gives μ_s = tan θ.
Карта 69
Въпрос
In an inertial frame, what determines the acceleration of a fixed-mass system's center of mass?
Отговор
The net external force divided by the system's total mass. Internal force pairs cannot change the center-of-mass motion of the whole system.
Карта 70
Въпрос
Which tension components act for a conical pendulum?
Отговор
The vertical component balances weight, and the horizontal component supplies centripetal force. The bob moves in a horizontal circle.
Карта 71
Въпрос
What does apparent weight measure for an object supported by one surface?
Отговор
The normal-force magnitude exerted by that support. It can differ from gravitational force when the object accelerates.
Карта 72
Въпрос
How are several forces combined to find net force?
Отговор
Add them as vectors, component by component. Opposing components subtract according to the chosen signs.
Карта 73
Въпрос
Why is tension uniform along one continuous ideal string?
Отговор
Every massless segment must have zero net force in the ideal model. Without frictional contact or a massive pulley changing it, the tension magnitude stays the same throughout the string.
Карта 74
Въпрос
A 0.5 kg object moves at 4 m/s in a circle of radius 2 m. What inward net force is required?
Отговор
4 N. F_in = mv²/r = 0.5 × 16 / 2.
Карта 75
Въпрос
What local equivalence links a uniform gravitational field with a uniformly accelerating reference frame?
Отговор
A uniform gravitational field and a uniformly accelerating reference frame can produce the same local mechanical effects. Local observations alone may not distinguish them.
Карта 76
Въпрос
For the same net force, what happens to acceleration if mass doubles?
Отговор
Acceleration is halved. From a = ΣF/m, acceleration is inversely proportional to mass.
Карта 77
Въпрос
How do static and kinetic friction coefficients usually compare for the same pair of surfaces?
Отговор
Typically μ_s > μ_k. Starting sliding usually requires a larger friction threshold than maintaining it.
Карта 78
Въпрос
How are radial and tangential acceleration combined when circular speed changes?
Отговор
Add the perpendicular components as vectors. The total magnitude is √(a_c² + a_t²).
Карта 79
Въпрос
A spherically symmetric planet has twice Earth's mass and the same radius. How does its surface g compare with Earth's?
Отговор
It is twice as large. Surface field strength follows g = GM/R².
Карта 80
Въпрос
Does a force have to point in the direction of motion?
Отговор
No. A force points in the direction of the interaction; it may speed up, slow down, or turn the object.
Карта 81
Въпрос
Where is the center of mass of a uniform object with a symmetric mass distribution?
Отговор
At its geometric center of symmetry. Symmetry lets opposite mass elements balance without a detailed sum.
Карта 82
Въпрос
How are speed, period, and frequency related in uniform circular motion?
Отговор
v = 2πr/T = 2πrf, with T = 1/f. One cycle covers one circumference.
Карта 83
Въпрос
Why is an object apparently weightless in free fall?
Отговор
Its support force is zero while it and its surroundings accelerate together under gravity. Gravity still acts.
Карта 84
Въпрос
Can forces balance along one axis while an object accelerates along another?
Отговор
Yes. Zero net force in one component gives zero acceleration only in that direction; another component can remain unbalanced.
Карта 85
Въпрос
Why don't Newton's third-law forces cancel on one object's free-body diagram?
Отговор
Only one force in the pair acts on that object. The partner force belongs on the other object's diagram.
Карта 86
Въпрос
On a frictionless banked curve, which force components create vertical balance and inward acceleration?
Отговор
The normal force's vertical component balances weight, while its horizontal component supplies the inward net force.
Карта 87
Въпрос
What motion results when the net force on an object is zero in an inertial frame?
Отговор
Constant velocity. Rest is the special case with constant velocity equal to zero.
Карта 88
Въпрос
A 3 kg cart has a net horizontal force of 12 N. What is its acceleration?
Отговор
4 m/s². Use a = ΣF/m = 12/3.
Карта 89
Въпрос
What does the observed equivalence of inertial and gravitational mass imply for free fall?
Отговор
Free-fall acceleration is independent of the falling object's mass. Inertial and gravitational mass are proportional and conventionally assigned equal numerical values.
Карта 90
Въпрос
Does friction in the simple dry-friction model depend on apparent contact area?
Отговор
No. For a fixed normal force and the same contacting materials, the model treats friction magnitude as independent of apparent contact area.
Карта 91
Въпрос
When should Hooke's-law predictions be treated cautiously?
Отговор
When deformation leaves the spring's linear elastic range. Force may no longer be proportional to displacement.
Карта 92
Въпрос
What bank angle θ supports speed v on an ideal frictionless curve of radius r?
Отговор
tan θ = v²/(rg). The result assumes no vertical acceleration and no friction.
Карта 93
Въпрос
Why do internal forces cancel when finding the net force on a complete system?
Отговор
They occur in equal-and-opposite pairs between system parts. Each pair sums to zero in the system's force total.
Карта 94
Въпрос
An elevator moves downward at constant speed. How does the scale reading compare with weight?
Отговор
It equals the weight. Constant velocity means zero acceleration and N - mg = 0.
Карта 95
Въпрос
What assumptions let an ideal pulley redirect a string without changing its tension magnitude?
Отговор
The pulley is massless and frictionless, and the string is ideal. It changes the tension's direction while the magnitude stays the same on both sides.
Карта 96
Въпрос
What does inertia describe?
Отговор
An object's resistance to changes in velocity. Mass measures translational inertia.
Карта 97
Въпрос
For the same fixed-mass object or system across all measurements, what does the slope of a net-force-versus-acceleration graph represent?
Отговор
Its mass. Written as ΣF = ma, the graph has slope m when the object or system and its mass stay fixed.
Карта 98
Въпрос
Does zero net force mean no forces act?
Отговор
No. Several forces can act and cancel vectorially.
Карта 99
Въпрос
What is the common model for kinetic-friction magnitude?
Отговор
f_k = μ_kN. It applies while the surfaces slide under the model's assumptions.
Карта 100
Въпрос
How could hanging masses measure the spring constant of one ideal spring?
Отговор
At static equilibrium, record the spring's extension for several known weights and graph mg versus extension. Keep the same spring in its linear range; the slope is k.
Карта 101
Въпрос
For the same object at the same circular radius, how does required inward net force change if speed doubles?
Отговор
It becomes four times as large. F_in = mv²/r depends on speed squared.
Карта 102
Въпрос
Where is the center of mass of two point masses on an x-axis?
Отговор
At x_cm = (m₁x₁ + m₂x₂)/(m₁ + m₂). It lies closer to the larger mass.
Карта 103
Въпрос
Why must net force, rather than one selected force, be used in ΣF = ma?
Отговор
All external forces contribute to acceleration. Ignoring a force changes the vector sum and the prediction.
Карта 104
Въпрос
Why can tension vary along a hanging chain with nonnegligible mass?
Отговор
Higher sections must support and accelerate more chain below them. Newton's third law still applies locally to each interaction; it does not make tension uniform everywhere.
Карта 105
Въпрос
What makes a reference frame inertial?
Отговор
An object with zero net force has constant velocity in that frame. A frame accelerating relative to an inertial frame is noninertial.
Карта 106
Въпрос
How could carts test the proportionality between acceleration and net force?
Отговор
Keep total mass constant, vary the applied net force, and graph acceleration versus force. A line through the origin supports a ∝ ΣF.
Карта 107
Въпрос
How does Kepler's third-law scaling compare two satellites in circular orbits at center-to-center radii r when their masses are negligible relative to the same fixed central mass?
Отговор
T² ∝ r³. The circular orbit with the larger center-to-center radius has the longer period.
Карта 108
Въпрос
Which direction does kinetic friction act?
Отговор
Opposite the relative sliding of the contacting surfaces. It is not automatically opposite the object's velocity in every frame.
Карта 109
Въпрос
What does the slope of a spring-force-versus-displacement graph give?
Отговор
-k when signed force is graphed against signed displacement. The slope magnitude is the spring constant.
Карта 110
Въпрос
What is the minimum speed at the top of an ideal vertical loop of radius r when gravity alone supplies the inward force?
Отговор
v_min = √(gr). At the threshold, the support force or tension is zero.
Карта 111
Въпрос
What is translational kinetic energy?
Отговор
Energy associated with an object's translational motion. For a point-like object, K = ½mv².
Карта 112
Въпрос
How is work by a constant force calculated when its point of application undergoes a straight displacement?
Отговор
W = Fd cos θ. Here d is the displacement of the force's point of application, and θ is the angle between the force and that displacement.
Карта 113
Въпрос
What does power measure?
Отговор
The rate of energy transfer or conversion. P_avg = ΔE_transferred/Δt; when work is the relevant transfer, P_avg = W/Δt.
Карта 114
Въпрос
What does conservation of energy say for an isolated system?
Отговор
The system's total energy stays constant. Energy may change form or move among system parts, but it is not created or destroyed.
Карта 115
Въпрос
Can translational kinetic energy be negative?
Отговор
No. Mass is positive and speed is squared, so translational kinetic energy is zero or positive.
Карта 116
Въпрос
What does negative work by a force mean?
Отговор
The force makes a negative contribution to the system's kinetic-energy change. Its component opposes the displacement of its point of application; potential energy may rise while total mechanical energy stays constant.
Карта 117
Въпрос
What is the near-surface change in gravitational potential energy?
Отговор
ΔU_g = mgΔy. It applies when g can be treated as constant.
Карта 118
Въпрос
When is a chosen system's mechanical energy K + U conserved?
Отговор
When no net energy crosses the system boundary and no internal process converts energy in either direction between mechanical and nonmechanical forms. If either condition fails, K + U can change even though total energy still balances for the system plus surroundings.
Карта 119
Въпрос
What is the SI unit of power?
Отговор
The watt, W. One watt equals one joule per second.
Карта 120
Въпрос
For an object modeled as a particle, what connects net work by all forces to its change in translational kinetic energy?
Отговор
The work–energy theorem: W_net = ΔK. Under the particle model, positive net work raises translational kinetic energy and negative net work lowers it. A rotating rigid system requires total kinetic energy and work at the forces' points of application.
Карта 121
Въпрос
A ball falls from rest through height h near a planet's surface. For the ball–planet system, g is constant and air resistance is negligible. What speed does energy conservation predict?
Отговор
v = √(2gh). The system's mgh decrease in gravitational potential energy becomes ½mv².
Карта 122
Въпрос
Does choosing a different zero level for potential energy change physical predictions?
Отговор
No. Only potential-energy differences enter measurable energy changes.
Карта 123
Въпрос
Can an engine do the same work with different average power?
Отговор
Yes. Doing the same work in less time requires greater average power.
Карта 124
Въпрос
When does a constant nonzero force do zero work over an interval?
Отговор
When its point of application has zero displacement or its displacement is perpendicular to the force. Then W = Fd cos θ is zero.
Карта 125
Въпрос
A particle-modeled block slides down a fixed frictionless track. Does the path shape affect its final speed at a given lower height?
Отговор
No. With only gravity doing work, the potential-energy change depends on height, not path.
Карта 126
Въпрос
How does translational kinetic energy change if speed doubles at constant mass?
Отговор
It becomes four times as large. Kinetic energy depends on v².
Карта 127
Въпрос
What is the elastic potential energy of an ideal spring displaced by a signed amount x from its relaxed or natural length, with U_s = 0 there?
Отговор
U_s = ½kx². Choosing zero energy at the relaxed length gives the same stored energy for equal-magnitude extension or compression.
Карта 128
Въпрос
What does signed area under a force-component-versus-position graph represent when position tracks that force's point of application?
Отговор
Work done by that force along the measured coordinate. Area below the position axis counts as negative work under the graph's sign convention.
Карта 129
Въпрос
A chosen system starts with 20 J of mechanical energy and converts 6 J of it into thermal energy, with no energy crossing the boundary. How much mechanical energy remains?
Отговор
14 J. The 6 J thermal-energy increase matches the mechanical-energy decrease.
Карта 130
Въпрос
What shape does a translational-kinetic-energy-versus-speed graph have for fixed mass?
Отговор
The right-hand half of an upward-opening parabola through the origin. Speed is nonnegative, and K is proportional to v², not v.
Карта 131
Въпрос
A machine transfers 600 J in 3 s. What is its average power?
Отговор
200 W. Divide energy transferred by elapsed time.
Карта 132
Въпрос
Why does the normal force do no work on a nonrotating block sliding across a fixed horizontal floor?
Отговор
The force is perpendicular to the horizontal displacement of its points of application. Their dot product is zero in this pure-translation model.
Карта 133
Въпрос
A coaster modeled as a particle moves on a fixed frictionless track. Where is its speed greatest?
Отговор
At the lowest accessible position. Gravitational potential energy is smallest there, so kinetic energy is largest.
Карта 134
Въпрос
Two objects have equal mass and velocities of equal magnitude but opposite direction. How do their translational kinetic energies compare?
Отговор
They are equal. Kinetic energy uses speed and has no direction.
Карта 135
Въпрос
What makes work by a conservative force path independent?
Отговор
It depends only on the initial and final configurations. Any two paths between the same endpoints give the same conservative-force work.
Карта 136
Въпрос
A 10 N force acts while its point of application moves 3 m in the force direction. How much work does the force do?
Отговор
30 J. Here θ = 0, so W = Fd = 10×3.
Карта 137
Въпрос
How is total potential energy built for a system with several interacting pairs?
Отговор
Add the potential energy assigned to each relevant pair. Count each interaction pair once and use one consistent reference choice.
Карта 138
Въпрос
How should external work appear in an energy equation?
Отговор
As energy transferred across the system boundary. A useful form is ΔE_system = W_external + other transfers.
Карта 139
Въпрос
How does a spring launch problem combine energy forms?
Отговор
Initial elastic energy becomes kinetic energy and possibly gravitational or thermal energy. Write only the forms present in the chosen initial and final states.
Карта 140
Въпрос
For a constant force parallel to the velocity of its point of application, how is instantaneous mechanical power calculated?
Отговор
P = Fv. More generally, P = F·v_point, so only the force component along that point's velocity contributes.
Карта 141
Въпрос
How does translational kinetic energy change if mass triples at constant speed?
Отговор
It triples. Kinetic energy is directly proportional to mass.
Карта 142
Въпрос
How much net work does a conservative force do around a path that returns to the initial configuration?
Отговор
Zero. The initial and final potential energies are the same.
Карта 143
Въпрос
Where is stable equilibrium on a potential-energy-versus-position graph?
Отговор
At a local minimum. Small displacements produce forces that point back toward the minimum.
Карта 144
Въпрос
Which displacement belongs in the work done by a force on a rigid object?
Отговор
The displacement of that force's point of application. Using the center-of-mass displacement can be wrong when the object also rotates.
Карта 145
Въпрос
What happens to mechanical energy when kinetic friction acts inside the chosen system?
Отговор
Some mechanical energy becomes thermal energy. The broader system's total energy still balances.
Карта 146
Въпрос
A nonrotating particle falls from rest through vertical drop h under constant g. If its gravitational-potential decrease becomes only translational kinetic energy, with no other energy changes, what graph linearizes final speed?
Отговор
Graph v² versus drop height h. Under those conditions, v² = 2gh, so the slope should be 2g.
Карта 147
Въпрос
If two students start and finish a stair climb at the same speeds, how could data compare their average mechanical output power against gravity?
Отговор
Measure each student's mass, vertical rise, and climb time, then calculate mgh/t. Equal initial and final speeds make ΔK = 0; if ΔK is negligible, the result is an approximation. This is mechanical output power against gravity, not metabolic input power.
Карта 148
Въпрос
How can force-sensor data measure work when force changes as its point of application moves?
Отговор
Graph the force component along the motion against the point-of-application position and find the signed area. A rectangle formula isn't enough for a varying force.
Карта 149
Въпрос
Why is potential energy assigned to a system rather than one isolated object?
Отговор
It belongs to an interaction between system parts. Gravitational potential energy, for example, belongs to the object–Earth system.
Карта 150
Въпрос
How can work by a nonconservative force depend on path?
Отговор
Different routes can have different force histories or path lengths. Kinetic-friction work, for example, can change with distance traveled.
Карта 151
Въпрос
A 2 kg cart moves at 3 m/s. What is its translational kinetic energy?
Отговор
9 J. K = ½(2)(3²) = 9 J.
Карта 152
Въпрос
A block slides distance d across a stationary surface while constant kinetic friction f_k opposes its displacement. What work does friction do on the block?
Отговор
W_f = -f_k d. The negative sign follows from friction pointing opposite the block's displacement in this stated setup.
Карта 153
Въпрос
A 2 kg object rises 5 m where g = 10 m/s². What is ΔU_g?
Отговор
+100 J. ΔU_g = mgΔy = 2 × 10 × 5.
Карта 154
Въпрос
Why are energy bar charts useful?
Отговор
They make initial energy, final energy, and transfers explicit. A correct chart respects the chosen system and reference levels.
Карта 155
Въпрос
A motor lifts the same load through the same height twice as fast. Both lifts begin and end at the same speeds and have equal or negligible dissipative losses. How do the motor's mechanical output work and average power compare?
Отговор
The mechanical output work is unchanged, while average power doubles. The two lifts have the same ΔU_g, the same ΔK, and the same losses, so the same output energy is delivered in half the time.
Карта 156
Въпрос
A nonrotating 1 kg block starts from rest and receives 18 J of net work. What speed does it reach?
Отговор
6 m/s. For this pure-translation model, ΔK = 18 J = ½(1)v².
Карта 157
Въпрос
Why is gravitational potential energy lower when two attracting point masses—or nonoverlapping spherical bodies—are closer in the inverse-square model?
Отговор
Energy must be supplied to separate them. With zero chosen at infinite center-to-center separation, U_g = -GMm/r.
Карта 158
Въпрос
What does a steep potential-energy graph imply about force magnitude in one dimension?
Отговор
A large force magnitude. Force points toward decreasing potential energy and corresponds to the negative slope of U(x).
Карта 159
Въпрос
An ideal spring with k = 80 N/m is compressed 0.50 m from its relaxed length. With U_s = 0 at that length, what elastic energy is stored?
Отговор
10 J. U_s = ½(80)(0.50²).
Карта 160
Въпрос
A constant 50 N force acts while its point of application moves at 4 m/s in the force direction. What mechanical power is delivered?
Отговор
200 W. P = Fv_point = 50 × 4.
Карта 161
Въпрос
If potential energy decreases by 30 J and no energy crosses the system boundary, what happens to the other energy forms?
Отговор
They increase by a total of 30 J. Often kinetic energy rises, but thermal or other forms may share the increase.
Карта 162
Въпрос
Does an object's translational kinetic energy depend on the reference frame?
Отговор
Yes. Different inertial observers can measure different speeds and therefore different K = ½mv² for the same object.
Карта 163
Въпрос
Why can work depend on the system boundary?
Отговор
Changing the system can reclassify energy transfer. For example, friction may be external work on one system but internal thermal-energy conversion in a larger system.
Карта 164
Въпрос
A force-component-versus-position graph for the force's point of application forms a triangle of base 4 m and height 6 N above the axis. What work does it show?
Отговор
12 J. The signed area is ½×4×6.
Карта 165
Въпрос
A motor transfers 50 J into a chosen system while another device transfers 12 J out. What is the net system-energy change?
Отговор
+38 J. Add the signed transfers across the boundary: 50 J - 12 J.
Карта 166
Въпрос
What is the clearest first step in an energy-conservation problem?
Отговор
Choose the system and the initial and final states. That choice determines which energies and transfers belong in the equation.
Карта 167
Въпрос
Why can energy methods solve some problems without finding time?
Отговор
Energy connects states through position, speed, and transfers. Time is absent unless power or a time-dependent process matters.
Карта 168
Въпрос
Why can a force's instantaneous mechanical power be zero while the force is nonzero?
Отговор
Its point of application may be instantaneously at rest, or the force may be perpendicular to that point's velocity. In either case F·v_point = 0.
Карта 169
Въпрос
What is the SI unit of kinetic energy?
Отговор
The joule, J. One joule equals 1 kg·m²/s².
Карта 170
Въпрос
How is work by a conservative force related to potential-energy change?
Отговор
W_conservative = -ΔU. When the conservative force does positive work, potential energy falls.
Карта 171
Въпрос
Where is unstable equilibrium on a potential-energy-versus-position graph?
Отговор
At a local maximum. A small displacement produces a force that pushes the system farther away.
Карта 172
Въпрос
For a particle moving in a circle at constant speed, does the inward net force change its translational kinetic energy?
Отговор
No. The inward net force is perpendicular to the particle's instantaneous velocity, so its net work is zero and it changes the velocity's direction rather than its magnitude.
Карта 173
Въпрос
Why should thermal energy not be written as a force?
Отговор
Thermal energy is an energy store, not an interaction force. Friction is the interaction that converts or transfers energy.
Карта 174
Въпрос
How could a ramp experiment test mechanical-energy conservation for a cart–Earth system when the cart is modeled as a particle?
Отговор
Measure speed and height at several points, calculate K + U_g with one consistent zero level, and compare within uncertainty. Systematic drift suggests unmodeled energy transfer or conversion.
Карта 175
Въпрос
According to the plotted power's definition and sign convention, what does signed area under a power-versus-time graph represent?
Отговор
Energy transferred or converted over the interval. Interpret positive and negative areas using the graph's stated sign convention and what its power represents.
Карта 176
Въпрос
What is linear momentum?
Отговор
p = mv. Momentum is a vector in the direction of velocity and uses SI units kg·m/s.
Карта 177
Въпрос
How is a multi-object system's total momentum found?
Отговор
Add every object's momentum as a vector. In one dimension, add signed values.
Карта 178
Въпрос
For a chosen object or system, what is external impulse?
Отговор
The change in its momentum: J_external = Δp. For constant net external force, J_external = F_net,external Δt.
Карта 179
Въпрос
What experimental uncertainty matters strongly when comparing collision kinetic energies?
Отговор
Velocity uncertainty. Because K depends on v², small speed errors can produce larger relative energy errors.
Карта 180
Въпрос
Why can two objects bounce apart yet still collide inelastically?
Отговор
Bouncing does not guarantee kinetic-energy conservation. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.
Карта 181
Въпрос
A 3 kg cart moves right at 4 m/s. What is its momentum if right is positive?
Отговор
+12 kg·m/s. p = mv = 3 × 4.
Карта 182
Въпрос
Why can momentum be negative while kinetic energy cannot?
Отговор
Momentum carries direction through velocity's sign. Kinetic energy depends on speed squared.
Карта 183
Въпрос
When is a system's total linear momentum conserved?
Отговор
When the net external impulse is zero or negligible during the interval. Internal impulses cancel in the system total.
Карта 184
Въпрос
Two equal masses collide elastically in one dimension; one is initially at rest. What commonly happens?
Отговор
They exchange velocities. The incoming mass stops and the other leaves with its speed under the ideal conditions.
Карта 185
Въпрос
Can total kinetic energy increase in an explosion?
Отговор
Yes. Stored internal energy can become kinetic energy. Total momentum is conserved for a defined system with zero or negligible net external impulse, while total energy remains conserved for the system plus surroundings.
Карта 186
Въпрос
How is total momentum related to center-of-mass velocity?
Отговор
p_total = Mv_cm. M is the system's total mass.
Карта 187
Въпрос
How does a nonzero external impulse affect system momentum?
Отговор
It changes total momentum by that impulse. J_external = Δp_system.
Карта 188
Въпрос
Two carts start at rest and push apart with negligible external horizontal impulse. How do their final momenta compare?
Отговор
They are equal in magnitude and opposite in direction. The system began with zero total momentum.
Карта 189
Въпрос
What are equivalent SI units for impulse?
Отговор
N·s and kg·m/s. Both represent a change in momentum.
Карта 190
Въпрос
What defines an elastic collision?
Отговор
Both total momentum and total kinetic energy are conserved for the chosen isolated system. Individual objects may exchange both quantities.
Карта 191
Въпрос
How can a force sensor and motion detector test the impulse–momentum theorem for one cart?
Отговор
Account for every external force component along the measured axis, compare the net-force–time area with m(v_f - v_i), and include uncertainty. Agreement supports J_external = Δp.
Карта 192
Въпрос
A person jumps right from a stationary boat. Neglecting external horizontal impulse, which way does the boat move?
Отговор
Left. The person and boat acquire opposite momenta so total momentum remains zero.
Карта 193
Въпрос
Why must momentum signs be kept through an impulse calculation?
Отговор
Impulse changes a vector quantity. Reversal can make Δp larger than either momentum magnitude alone.
Карта 194
Въпрос
What defines a perfectly inelastic collision?
Отговор
The objects stick together after impact. Momentum is conserved in an isolated system, but kinetic energy decreases as much as the constraints allow.
Карта 195
Въпрос
Why can momentum be conserved during a collision even when large forces act?
Отговор
For a defined system with zero or negligible net external impulse, the large collision forces are internal. Their equal-and-opposite impulses cancel within that system.
Карта 196
Въпрос
Two objects have equal speed. Which has the larger momentum magnitude?
Отговор
The object with larger mass. At equal speed, momentum is proportional to mass.
Карта 197
Въпрос
How is momentum conservation written for a two-dimensional isolated interaction?
Отговор
Conserve components separately: Σp_x,i = Σp_x,f and Σp_y,i = Σp_y,f. Both component equations must hold for the same interaction.
Карта 198
Въпрос
For a chosen object or system, how is average net external force related to impulse?
Отговор
F_avg,external = Δp/Δt. For the same momentum change, a longer interaction time gives a smaller average force.
Карта 199
Въпрос
Which conservation law alone can determine the shared final velocity of a sticking collision?
Отговор
Linear momentum conservation, if external impulse is negligible. Kinetic energy is not conserved in the sticking process.
Карта 200
Въпрос
Two equal momentum vectors point along +x and +y. What direction does their total momentum point?
Отговор
At 45° between the positive axes. Equal perpendicular components produce that resultant direction.
400 карти
AP Physics 1 Flashcards: Complete 8-Unit Course Review
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Карта 201
Въпрос
If external impulse during a collision is small but not zero, what should experimental data show?
Отговор
Final total momentum should be close to, but not exactly equal to, initial total momentum. The difference estimates external impulse.
Карта 202
Въпрос
A force–time pulse has the same area but twice the peak force and half the duration. How does its impulse change?
Отговор
It does not change. Impulse depends on total signed area, not peak force alone.
Карта 203
Въпрос
A 1 kg cart at 4 m/s sticks to an identical stationary cart. If external impulse is negligible, how does final kinetic energy compare with the initial 8 J?
Отговор
It is 4 J, half the initial value. The 4 J decrease in translational kinetic energy becomes internal or thermal energy through deformation, and some energy may be carried by sound.
Карта 204
Въпрос
How can a nearly frictionless cart track improve a momentum-conservation test?
Отговор
It reduces external horizontal impulse during the collision. That makes the two-cart system closer to isolated.
Карта 205
Въпрос
How does an object's momentum change if its speed doubles at constant mass?
Отговор
Its momentum magnitude doubles. Momentum depends linearly on speed.
Карта 206
Въпрос
For a chosen object or system, what does signed area under its net-external-force-versus-time graph represent?
Отговор
External impulse, which equals the change in that object's or system's momentum. Area below the time axis contributes negative impulse under the graph's sign convention.
Карта 207
Въпрос
A firework at rest explodes into two pieces with negligible external impulse. If one piece has twice the mass, how do the piece speeds compare?
Отговор
The heavier piece moves at half the speed of the lighter piece. Their momentum magnitudes must match.
Карта 208
Въпрос
Why is sticking evidence of an inelastic collision?
Отговор
The objects share one final velocity, while some translational kinetic energy becomes internal or thermal energy through deformation. Translational kinetic energy is not conserved.
Карта 209
Въпрос
Can a moving two-object system have zero total momentum?
Отговор
Yes. Equal and opposite momenta cancel even though each object is moving.
Карта 210
Въпрос
A constant 6 N net external force acts on a chosen object for 0.5 s. What impulse does it deliver?
Отговор
3 N·s in the force direction. Multiply the net external force by the interaction time.
Карта 211
Въпрос
What does a momentum-versus-velocity graph's slope represent for one object?
Отговор
Its mass. The relationship p = mv is linear through the origin.
Карта 212
Въпрос
A 2 kg cart at +3 m/s sticks to a 1 kg cart at rest. If external horizontal impulse is negligible, what is their final velocity?
Отговор
+2 m/s. Momentum conservation gives (2×3 + 1×0)/(2+1).
Карта 213
Въпрос
An isolated two-dimensional interaction has known initial total momentum p_total,i and known first outgoing momentum p₁,f. How is the second outgoing momentum found?
Отговор
Subtract component by component: p₂,f = p_total,i - p₁,f. Thus p₂x,f = p_total,x,i - p₁x,f, with the same subtraction for y.
Карта 214
Въпрос
A 2 kg ball changes velocity from +3 m/s to -1 m/s. What impulse acts on it?
Отговор
-8 N·s. Δp = m(v_f - v_i) = 2(-1 - 3).
Карта 215
Въпрос
What remains conserved in an isolated inelastic collision?
Отговор
Total momentum. Some kinetic energy becomes internal or thermal energy through deformation, and some may be carried by sound.
Карта 216
Въпрос
Why does choosing both colliding objects as the system simplify momentum analysis?
Отговор
Their contact forces become internal. Only external impulse can change the system total.
Карта 217
Въпрос
For a chosen object or system, what does the slope of its momentum-versus-time graph represent?
Отговор
Net external force. A steeper slope means a larger force in the slope's signed direction.
Карта 218
Въпрос
Why do airbags reduce injury force during a stop?
Отговор
They increase the stopping time for roughly the same momentum change. That lowers the average force.
Карта 219
Въпрос
A 1 kg cart at 4 m/s sticks to an identical stationary cart. If external impulse is negligible, what final speed do they share?
Отговор
2 m/s. Momentum 4 kg·m/s is shared by 2 kg.
Карта 220
Въпрос
For a defined collision system with zero or negligible net external impulse, how can before-and-after velocity measurements classify the collision?
Отговор
First verify total momentum within uncertainty, then compare total kinetic energy. Unchanged kinetic energy supports elastic behavior; any change beyond uncertainty means the collision isn't elastic, with a decrease indicating an ordinary inelastic collision.
Карта 221
Въпрос
What is angular displacement?
Отговор
The signed angle through which a rigid body rotates. In calculations, radians make the linear–angular relationships direct.
Карта 222
Въпрос
For a rigid body rotating about a chosen fixed axis, what does angular velocity measure?
Отговор
Signed angular displacement per time about that axis. Average angular velocity is ω_avg = Δθ/Δt under one sign convention.
Карта 223
Въпрос
For a rigid body rotating about a chosen fixed axis, what does angular acceleration measure?
Отговор
Change in signed angular velocity per time about that axis. Average angular acceleration is α_avg = Δω/Δt.
Карта 224
Въпрос
What does rotational inertia measure?
Отговор
Resistance to angular acceleration about a specified axis. It depends on mass and how that mass is distributed relative to the axis.
Карта 225
Въпрос
What is the lever arm in a torque calculation?
Отговор
The perpendicular distance from the axis to the force's line of action. It is not always the full distance to the contact point.
Карта 226
Въпрос
For a planar rigid object in an inertial frame, what two conditions give simultaneous translational and rotational equilibrium?
Отговор
ΣF_external = 0 and Στ_external = 0 about a fixed axis. Static equilibrium also requires the object to be at rest.
Карта 227
Въпрос
Two points lie on the same rotating rigid disk. Which rotational quantities are the same?
Отговор
They share angular displacement, angular velocity, and angular acceleration. Their linear speeds and accelerations can differ with radius.
Карта 228
Въпрос
How is rotational inertia found for a collection of point masses?
Отговор
I_total = Σmᵢrᵢ². Each rᵢ is that mass's perpendicular distance from the chosen axis.
Карта 229
Въпрос
What determines the magnitude of torque from one force about a chosen axis?
Отговор
τ = rF sin θ = r_perp F. The radius vector r runs from the axis to the force's point of application, θ is the angle between r and the force, and r_perp is the lever arm.
Карта 230
Въпрос
What is Newton's second law for a rigid system rotating about an axis fixed in an inertial frame?
Отговор
Στ_external = Iα when rotational inertia I about that axis is constant. Net external torque and angular acceleration use the same signed-axis convention.
Карта 231
Въпрос
For a point on a rigid body rotating about a fixed axis, how is signed arc displacement related to signed angular displacement in radians?
Отговор
Δs = rΔθ. Here r is the point's perpendicular distance from the fixed axis, and both displacements use matching sign conventions along the circular path.
Карта 232
Въпрос
In a planar rigid-body model, can an object with zero net external force and zero net external torque about its center of mass be moving?
Отговор
Yes. Its center of mass may translate at constant velocity while it rotates at constant angular velocity; the stated zero net force and center-of-mass torque don't require rest.
Карта 233
Въпрос
At an instant when ω ≠ 0, what do the signs of angular velocity and angular acceleration show about rotational speed?
Отговор
Matching signs mean the rotation speeds up; opposite signs mean it slows down. The sign convention chooses which rotation direction is positive.
Карта 234
Въпрос
How are clockwise and counterclockwise torques combined?
Отговор
Choose one direction as positive and add signed torques. Net torque is the algebraic sum about the same axis.
Карта 235
Въпрос
For the same rigid system with constant rotational inertia about the same axis fixed in an inertial frame, what happens if net-external-torque magnitude doubles?
Отговор
Angular-acceleration magnitude doubles. Under those conditions, |α| is directly proportional to |Στ_external|.
Карта 236
Въпрос
Why must an axis be named when stating rotational inertia?
Отговор
The same object has different rotational inertia about different axes. Mass distribution relative to the chosen axis changes.
Карта 237
Въпрос
For one rigid body rotating about a fixed axis, what does the slope of its angular-position-versus-time graph represent?
Отговор
Signed angular velocity about that axis. A constant slope means constant angular velocity under the graph's sign convention.
Карта 238
Въпрос
Why is torque's unit N·m not called a joule?
Отговор
Torque and energy are different physical quantities despite matching unit dimensions. Torque describes rotational effectiveness of a force.
Карта 239
Въпрос
A rigid wheel has constant I = 2 kg·m² about an axis fixed in an inertial frame and net external torque 8 N·m about that axis. What is its angular-acceleration magnitude?
Отговор
4 rad/s². |α| = |Στ_external|/I = 8/2.
Карта 240
Въпрос
Where can the weight of a rigid object be treated as acting in a uniform gravitational field?
Отговор
At the object's center of mass. That single force gives the same net gravitational force and torque.
Карта 241
Въпрос
For a point on a rigid body rotating about a fixed axis, how is tangential-speed magnitude related to angular velocity?
Отговор
v_t = r|ω|. Here r is the perpendicular distance from the fixed axis. Points farther from the axis move faster even though the rigid body has one angular velocity.
Карта 242
Въпрос
For constant angular acceleration about one fixed axis, what does ω = ω₀ + αt retrieve?
Отговор
Angular velocity after elapsed time t. Use signed angular quantities about that axis over an interval with constant α.
Карта 243
Въпрос
A free-body diagram for a rigid bar must support a torque calculation about a marked axis. What must it show besides each force's direction and magnitude?
Отговор
Each force's point of application or line of action relative to the axis. That geometry sets the lever arm and torque sign; omitting it can preserve the net-force picture while losing the net torque.
Карта 244
Въпрос
For the same rigid system about the same axis fixed in an inertial frame, what does the slope of a net-external-torque-versus-angular-acceleration graph represent?
Отговор
Its constant rotational inertia I about that axis. The graph follows Στ_external = Iα.
Карта 245
Въпрос
A thin hoop and solid disk have the same mass and radius and rotate about their central symmetry axes. With I_hoop = MR² and I_disk = ½MR², which has larger I?
Отговор
The hoop. More of its mass lies far from the axis.
Карта 246
Въпрос
Why can a rigid object have zero net external force but nonzero net external torque?
Отговор
External forces can cancel as vectors while acting along different lines. The resulting couple can still change the object's rotation.
Карта 247
Въпрос
Which constant-angular-acceleration equation connects angular velocity and angular displacement about one fixed axis without time?
Отговор
ω² = ω₀² + 2αΔθ. Use signed quantities about that axis over an interval with constant α.
Карта 248
Въпрос
A 10 N perpendicular force acts 0.40 m from a pivot. What torque magnitude does it produce?
Отговор
4 N·m. τ = rF for a perpendicular force.
Карта 249
Въпрос
For a rigid body rotating about a fixed axis, how is the signed tangential-acceleration component related to angular acceleration?
Отговор
For a positive tangent consistent with the angular sign convention, a_t = rα. Its alignment or opposition with velocity determines whether speed increases or decreases.
Карта 250
Въпрос
Why can two equal-mass rigid wheels have different angular-acceleration magnitudes under equal net-external-torque magnitudes about comparable axes fixed in an inertial frame?
Отговор
Their rotational inertias about those axes can differ because their mass distributions differ. Mass alone doesn't set rotational response.
Карта 251
Въпрос
For one rigid body rotating about a fixed axis, what does signed area under its angular-velocity-versus-time graph represent?
Отговор
Signed angular displacement about that axis. Area below the time axis contributes negative angular displacement under the graph's sign convention.
Карта 252
Въпрос
A rigid object rests on a support that is slowly tilted in uniform gravity. If gravity and support contact are its only external interactions, sufficient static friction prevents slipping, and the motion is quasistatic, what marks the onset of tipping?
Отговор
The object's center-of-mass vertical line reaches the edge of its support region. Beyond that point, gravity produces an unbalanced tipping torque.
Карта 253
Въпрос
A point is twice as far from a rigid wheel's fixed axis as another point. How do their tangential speeds compare?
Отговор
The farther point moves twice as fast. v_t is proportional to radius for their common angular-speed magnitude |ω|.
Карта 254
Въпрос
Does moving the chosen pivot change an individual force's torque?
Отговор
Yes. Torque depends on the axis, though a correctly solved physical prediction stays consistent.
Карта 255
Въпрос
How does the parallel-axis theorem relate rotational inertia to a parallel axis a distance d from the center of mass?
Отговор
I = I_cm + Md². Shifting the axis away from the center of mass increases rotational inertia.
Карта 256
Въпрос
How could an experiment determine a rigid wheel's constant rotational inertia about an axis fixed in an inertial frame?
Отговор
Apply several known signed net external torques about that axis, measure signed angular acceleration, and graph torque versus α. The slope is I.
Карта 257
Въпрос
For a point at perpendicular distance r > 0 from a rigid body's fixed rotation axis, what is the radial-acceleration magnitude?
Отговор
a_r = v_t²/r = rω². The acceleration points toward the axis. At r = 0, use a_r = rω² = 0; the quotient form isn't defined there.
Карта 258
Въпрос
How could a meterstick experiment test torque balance?
Отговор
Hang known forces at measured lever arms and compare signed r_perp F values at equilibrium. Repeat with different pivot choices.
Карта 259
Въпрос
For uniform rotation at frequency f, what is the angular-speed magnitude?
Отговор
|ω| = 2πf. One revolution is 2π rad, and uniform rotation has the same angular-speed magnitude throughout the cycle.
Карта 260
Въпрос
Why is choosing the pivot at an unknown support force often useful?
Отговор
That force then has zero lever arm and drops out of the torque equation. The physical equilibrium does not depend on the calculation shortcut.
Карта 261
Въпрос
Among parallel axes through or near a rigid object, which gives the minimum rotational inertia?
Отговор
The parallel axis through the center of mass. Any offset adds the positive term Md².
Карта 262
Въпрос
Compare rigid systems with constant rotational inertia about comparable axes fixed in an inertial frame. If net external torque is the same but I triples, what happens to angular acceleration?
Отговор
It becomes one-third as large. For each stated system, α = Στ_external/I.
Карта 263
Въпрос
A rigid wheel of radius 0.50 m has angular-speed magnitude 6 rad/s about its fixed axis. What is the rim speed?
Отговор
3 m/s. v_t = r|ω| = 0.50 × 6.
Карта 264
Въпрос
A 30 N child sits 2 m left of a seesaw pivot. If the seesaw's own weight acts through the pivot, where should a 20 N child sit on the right for balance?
Отговор
3 m from the pivot. Balance torque magnitudes: 30×2 = 20×r.
Карта 265
Въпрос
For constant angular acceleration about one fixed axis, what does Δθ = ω₀t + ½αt² retrieve?
Отговор
Angular displacement over elapsed time t. Use signed angular quantities about that axis; the equation combines the initial angular-velocity contribution with the change caused by constant α.
Карта 266
Въпрос
A 20 N force acts at 30° to a radius vector of magnitude 0.60 m from a chosen axis. What torque magnitude results?
Отговор
6 N·m. |τ| = rF sin θ = 0.60 × 20 × sin 30°.
Карта 267
Въпрос
How does moving mass farther from a rotation axis affect rotational inertia?
Отговор
It increases rotational inertia strongly. For a point mass, I = mr².
Карта 268
Въпрос
How can angular-acceleration data compare two rigid objects' constant rotational inertias about comparable axes fixed in an inertial frame?
Отговор
Apply the same measured net-external-torque magnitude about each axis and compare |α|. The object with smaller angular-acceleration magnitude has larger I.
Карта 269
Въпрос
Why must angular displacement be in radians for Δs = rΔθ?
Отговор
Radians define angle as arc length divided by radius. Degree measure would require a conversion factor.
Карта 270
Въпрос
When does a nonzero force produce zero torque about an axis?
Отговор
When its line of action passes through the axis. The lever arm is then zero.
Карта 271
Въпрос
What is angular momentum for a rigid object rotating about an axis fixed in an inertial frame?
Отговор
L = Iω about that axis. Use one signed-axis convention consistently for L and ω.
Карта 272
Въпрос
What magnitude relation holds for a planar, constant-radius rigid object whose center of mass lies on its rolling axis when it rolls without slipping on a stationary surface?
Отговор
v_cm = R|ω|. Here R is the constant rolling radius; the contact point is instantaneously at rest relative to the surface.
Карта 273
Въпрос
For a rigid system rotating about an axis fixed in an inertial frame, how is work by a constant torque about that axis related to angular displacement?
Отговор
W = τΔθ when torque and angular displacement use the same signed axis. The angle must be in radians.
Карта 274
Въпрос
For point masses—or nonoverlapping spherical bodies—M and m separated center to center by r, what is gravitational potential energy with zero at infinity?
Отговор
U_g = -GMm/r. The negative sign reflects U_g = 0 at infinity and attraction. In an isolated gravity-only inverse-square system, total mechanical energy determines binding: E < 0 is bound, while E ≥ 0 is unbound.
Карта 275
Въпрос
When is a chosen system's angular momentum about an axis fixed in an inertial frame conserved?
Отговор
When net external torque on the system about that axis is zero or negligible over the interval. Internal torques cannot change the system total.
Карта 276
Въпрос
What does kinetic friction do to mechanical energy while a wheel slips on a stationary surface?
Отговор
It converts mechanical energy into internal or thermal energy while the surfaces slide. Use qualitative energy accounting here; no no-slip relation connects the magnitudes v_cm and R|ω| during the slip.
Карта 277
Въпрос
What is the angular-momentum magnitude of a translating point object about a chosen fixed point in an inertial frame?
Отговор
L = mvr sin θ = r_perp mv. Here r points from the chosen point to the object, v is its speed, and θ is the angle between them. The SI unit is kg·m²/s.
Карта 278
Въпрос
For a satellite of negligible mass relative to a fixed central body, how do speed and energy change along one gravity-only elliptical orbit?
Отговор
Speed and kinetic energy are greatest near the central body, while gravitational potential energy is greatest farther away. Total mechanical energy stays constant.
Карта 279
Въпрос
What is a rigid body's rotational kinetic energy about a fixed axis?
Отговор
K_rot = ½Iω². It depends on rotational inertia about that axis and angular speed.
Карта 280
Въпрос
Two planar rigid objects with constant rolling radii and centers of mass on their rolling axes are released from rest on the same fixed incline. Each rolls without slipping under gravity and its contact forces, with no other applied force or torque and negligible dissipation. Which accelerates faster: the one with smaller or larger I_cm/(MR²)?
Отговор
The one with smaller I_cm/(MR²). Here I_cm is rotational inertia about the center of mass, M is total mass, and R is that object's constant rolling radius. Under the stated model, a_cm = g sin θ/(1 + I_cm/(MR²)).
Карта 281
Въпрос
How could a rotating-platform experiment test angular-momentum conservation about the platform's axis, treated as fixed in the lab's inertial frame?
Отговор
Choose the platform, rider, and moved masses as one system. In both the initial and final arrangements, wait until the rider and moved masses are stationary relative to the platform and the whole system co-rotates with one common signed angular velocity; then measure I_i, ω_i, I_f, and ω_f and compare I_iω_i with I_fω_f. Keep net external torque about the axis negligible, reduce bearing friction, and include uncertainty.
Карта 282
Въпрос
For a satellite of mass m negligible beside a fixed central mass M, how are K, U_g, and total mechanical energy E related in a gravity-only circular orbit at center-to-center radius r?
Отговор
K = -U_g/2 and E = U_g/2 = -K. Since U_g = -GMm/r, this gives K = GMm/(2r) and E = -GMm/(2r).
Карта 283
Въпрос
For a rigid system rotating about an axis fixed in an inertial frame, how is instantaneous mechanical power delivered by a torque about that axis related to angular velocity?
Отговор
P = τω for signed torque and angular velocity about the same axis. It is the rotational counterpart of P = F·v_point.
Карта 284
Въпрос
In a planar common-axis rigid-body model, what kinetic-energy expression applies to a body rolling without slipping, with I_cm and ω taken about the same axis through its center of mass?
Отговор
K = ½Mv_cm² + ½I_cmω². In this model, the rigid body's motion combines center-of-mass translation with rotation about one axis through the center of mass. I_cm and ω must refer to that same axis.
Карта 285
Въпрос
Does angular-momentum conservation require rotational kinetic-energy conservation?
Отговор
No. Internal work can change rotational kinetic energy while angular momentum stays constant.
Карта 286
Въпрос
Why do astronauts feel weightless in orbit even though gravity acts on them?
Отговор
They and their spacecraft are in continuous free fall together. Apparent weight is small because support forces are small.
Карта 287
Въпрос
Two wheels spin at the same angular speed. Which has more rotational kinetic energy?
Отговор
The wheel with larger rotational inertia. At common ω, K_rot is proportional to I.
Карта 288
Въпрос
For a chosen system, what does the slope of its angular-momentum-versus-time graph about an axis fixed in an inertial frame represent?
Отговор
Net external torque on the system about that axis. A constant slope means constant signed net external torque there.
Карта 289
Въпрос
A motor supplies 12 N·m of torque about a shaft axis fixed in the lab's inertial frame while the shaft turns in the torque direction at 10 rad/s. What mechanical power does it deliver?
Отговор
120 W. Using signed quantities about the shaft axis, P = τω = 12×10.
Карта 290
Въпрос
While a rigid wheel is slipping on a stationary surface, how are the magnitudes v_cm and R|ω| related?
Отговор
No no-slip equality applies. Their values evolve separately until friction may bring the contact point to rest relative to the surface.
Карта 291
Въпрос
A launched object has negligible mass relative to a fixed central mass M and starts at center-to-center radius r. What minimum speed lets it escape under gravity alone without further propulsion or drag?
Отговор
v_escape = √(2GM/r). At that threshold, total mechanical energy is zero with the object reaching infinity at zero speed.
Карта 292
Въпрос
In a planar common-axis rigid-body model, what kinetic-energy forms can a rigid body have when it translates and rotates about an axis through its center of mass?
Отговор
Both translational and rotational kinetic energy. The total is K = ½Mv_cm² + ½I_cmω², where I_cm and ω refer to the same axis through the center of mass.
Карта 293
Въпрос
For a chosen object or system, what is angular impulse about an axis fixed in an inertial frame?
Отговор
The change in that object or system's angular momentum about the axis. For constant net external torque, ΔL = τ_net,external Δt. Use the same axis and sign convention throughout. Angular impulse has units N·m·s, equivalent to kg·m²/s.
Карта 294
Въпрос
Two equal-mass planar rigid objects have constant rolling radii and centers of mass on their rolling axes. They start from rest at the same height and roll without slipping to the same lower endpoint with negligible dissipation. Why can their final speeds differ?
Отговор
Their rotational inertias divide the same decrease in gravitational potential energy differently between translation and rotation. A larger I_cm/(MR²) leaves less energy for translational speed, where I_cm is rotational inertia about the center of mass and R is rolling radius.
Карта 295
Въпрос
For a satellite of negligible mass relative to a fixed central body, how does angular momentum behave along one gravity-only elliptical orbit?
Отговор
It stays constant because gravity exerts zero torque about the central body. The satellite moves faster when closer and slower when farther away.
Карта 296
Въпрос
How does rotational kinetic energy change if angular speed doubles at fixed I?
Отговор
It becomes four times as large. Rotational kinetic energy depends on ω².
Карта 297
Въпрос
Why should external torque be evaluated about the same axis used for angular momentum?
Отговор
Both quantities depend on the chosen axis. Mixing axes breaks the conservation statement.
Карта 298
Въпрос
For a chosen object or system about an axis fixed in an inertial frame, what does signed area under its net-external-torque-versus-time graph represent?
Отговор
Angular impulse, equal to that object or system's ΔL about the axis. Use the graph's signed-axis convention. The area has units N·m·s, equivalent to kg·m²/s.
Карта 299
Въпрос
Why can static friction act on a rigid object rolling without slipping on a stationary rigid surface without necessarily dissipating mechanical energy?
Отговор
The contact point is instantaneously at rest relative to the surface, so there is no sliding. Static friction can still supply the torque needed for rolling.
Карта 300
Въпрос
For a satellite whose mass is negligible beside a fixed central mass M, what is its speed in a gravity-only circular orbit at center-to-center radius r?
Отговор
v = √(GM/r). Gravity supplies the inward net force.
Карта 301
Въпрос
A chosen system's included mass co-rotates with one common angular velocity before and after a change. If its rotational inertia about an axis fixed in an inertial frame doubles while net external torque about that axis is negligible, what happens to its angular speed?
Отговор
It halves. Because all included mass shares one angular velocity in each state, L = Iω applies. With the same axis and sign convention, angular-momentum conservation gives I_iω_i = I_fω_f.
Карта 302
Въпрос
For a rigid system rotating about an axis fixed in an inertial frame, what does signed area under its net-external-torque-versus-angular-position graph represent when angle is in radians?
Отговор
Net rotational work, equal to the system's change in rotational kinetic energy. Torque and angular position must use the same signed axis.
Карта 303
Въпрос
Why can't the rolling condition alone prove that friction points uphill or downhill?
Отговор
Friction direction depends on the tendency to slip and the applied forces or torques. Solve the dynamics instead of guessing from motion.
Карта 304
Въпрос
A satellite of mass m, negligible beside a fixed central mass M, follows a circular orbit at center-to-center radius r under gravity alone. What is its total mechanical energy?
Отговор
E = -GMm/(2r). A larger circular orbit has greater, less-negative energy even though its speed is lower.
Карта 305
Въпрос
A spinning student pulls masses closer to an axis fixed in the lab's inertial frame while net external torque about that axis is negligible. Why does angular speed increase?
Отговор
Rotational inertia decreases while angular momentum stays constant. Therefore Iω remains constant by increasing ω.
Карта 306
Въпрос
What makes simple harmonic motion a special kind of periodic motion?
Отговор
Its restoring force or torque is proportional to displacement and points toward equilibrium. Periodic motion alone does not guarantee this relationship.
Карта 307
Въпрос
What does the amplitude of an SHM displacement graph represent?
Отговор
The maximum distance from equilibrium. It is nonnegative even though displacement alternates sign.
Карта 308
Въпрос
How are period and frequency related?
Отговор
T = 1/f. Period is seconds per cycle; frequency is cycles per second, measured in hertz.
Карта 309
Въпрос
What is the period of a mass m on an ideal spring of constant k when spring mass and damping are negligible?
Отговор
T = 2π√(m/k). The motion must stay in the spring's linear SHM range.
Карта 310
Въпрос
For one-dimensional SHM, what is the equilibrium position?
Отговор
The position where the restoring force or torque—and therefore acceleration along the SHM coordinate—is zero. A stable equilibrium produces a restoring response after a small displacement.
Карта 311
Въпрос
How far apart in phase are displacement and velocity in SHM?
Отговор
One-quarter cycle. Velocity reaches an extremum when displacement crosses zero.
Карта 312
Въпрос
When can a simple pendulum be modeled as SHM?
Отговор
For small angular displacements. Then the restoring torque is approximately proportional to angular displacement.
Карта 313
Въпрос
An oscillator completes 12 cycles in 6 s. What are its frequency and period?
Отговор
f = 2 Hz and T = 0.5 s. Frequency is cycles per time, and period is its reciprocal.
Карта 314
Въпрос
For a horizontal ideal spring oscillator, what is potential energy at displacement x from its relaxed equilibrium length when U_s = 0 there?
Отговор
U_s = ½kx². It has the same value at +x and -x.
Карта 315
Въпрос
At the equilibrium position of SHM, is the oscillator necessarily at rest?
Отговор
No. The restoring force or torque and acceleration along the SHM coordinate are zero there, but speed is usually greatest.
Карта 316
Въпрос
How does a spring oscillator's period change if k becomes four times as large?
Отговор
The period is halved. T is proportional to 1/√k.
Карта 317
Въпрос
How are acceleration and displacement related along the SHM coordinate?
Отговор
a = -ω²x, where ω = 2πf is the oscillation's angular frequency. Here ω describes the oscillator's phase rate, not a rigid body's rotational angular velocity. The acceleration component along the SHM coordinate points toward equilibrium.
Карта 318
Въпрос
For a horizontal ideal spring oscillator with amplitude A, what is total mechanical energy when U_s = 0 at the relaxed equilibrium length?
Отговор
E = ½kA². It stays constant when dissipative effects are negligible.
Карта 319
Въпрос
In a small-angle pendulum, where are speed and gravitational potential energy greatest?
Отговор
Speed is greatest at the bottom; gravitational potential energy is greatest at the turning points. Energy trades between those forms.
Карта 320
Въпрос
How can frequency be read from an oscillation-versus-time graph?
Отговор
Measure the time between repeating equivalent points to find T, then use f = 1/T. Adjacent peaks are one period apart.
Карта 321
Въпрос
Why does an ideal mass–spring oscillator exhibit SHM?
Отговор
Its net restoring force is F_net = -kx, where x is displacement from equilibrium. The force is proportional to displacement and points back toward equilibrium.
Карта 322
Въпрос
A horizontal ideal spring has k = 50 N/m and amplitude 0.20 m. With U_s = 0 at equilibrium, what is the oscillator's total energy?
Отговор
1 J. E = ½(50)(0.20²).
Карта 323
Въпрос
At maximum positive displacement in SHM, what are velocity and acceleration?
Отговор
Velocity is zero; acceleration has maximum magnitude toward equilibrium. With positive displacement, acceleration is negative.
Карта 324
Въпрос
How does a spring oscillator's period change if its mass becomes four times as large?
Отговор
The period doubles. T is proportional to √m.
Карта 325
Въпрос
Why isn't uniform circular motion itself one-dimensional SHM?
Отговор
The object travels around a circle, not back and forth along one line. Its projection onto a diameter does follow SHM.
Карта 326
Въпрос
For the same ideal oscillator, how does total SHM energy change if amplitude doubles while k or mω² stays fixed?
Отговор
It becomes four times as large. Under those fixed system parameters, total energy is proportional to A².
Карта 327
Въпрос
In one-dimensional SHM, what are speed and acceleration along the SHM coordinate at equilibrium?
Отговор
Speed is maximum, while acceleration along the SHM coordinate is zero. The restoring force or torque vanishes there.
Карта 328
Въпрос
Does changing amplitude change the period of an ideal spring oscillator or small-angle pendulum?
Отговор
No within the ideal SHM model. The period depends on system parameters, not amplitude.
Карта 329
Въпрос
How is maximum speed related to amplitude and angular frequency in SHM?
Отговор
v_max = ωA. Maximum speed occurs at equilibrium.
Карта 330
Въпрос
For a horizontal ideal spring oscillator, how can kinetic energy at displacement x from equilibrium be found for amplitude A?
Отговор
K = ½k(A² - x²). Subtract spring potential energy from the constant total.
Карта 331
Въпрос
How far apart in phase are displacement and acceleration in SHM?
Отговор
Half a cycle, or 180°. When displacement is nonzero, acceleration has the opposite sign; at equilibrium, both are zero.
Карта 332
Въпрос
What is the period of a small-angle simple pendulum of length L when damping is negligible?
Отговор
T = 2π√(L/g). The simple-pendulum model uses a point-like bob on a light, inextensible string with a fixed support; bob mass doesn't affect the period.
Карта 333
Въпрос
If x(t) is at a positive maximum at t = 0, what qualitative pattern follows over one cycle?
Отговор
It crosses equilibrium moving negative at T/4, reaches negative maximum at T/2, returns through equilibrium at 3T/4, and reaches maximum positive displacement at T.
Карта 334
Въпрос
At equilibrium, how are a horizontal ideal spring oscillator's energies divided?
Отговор
Kinetic energy is maximum and spring potential energy is minimum. With x measured from equilibrium, U_s = 0 at x = 0.
Карта 335
Въпрос
An SHM object is at negative displacement and moving toward equilibrium. What signs do velocity and acceleration have if positive is right?
Отговор
Both are positive. Motion and restoring acceleration point right toward equilibrium.
Карта 336
Въпрос
How does a pendulum's period change if its length becomes nine times as large?
Отговор
The period triples. T is proportional to √L.
Карта 337
Въпрос
If SHM starts at maximum positive displacement, what equation gives its position?
Отговор
x(t) = A cos(2πft). A is amplitude, f is frequency, and t is elapsed time.
Карта 338
Въпрос
What feature would rule out ideal SHM in a force-versus-displacement-from-equilibrium graph?
Отговор
A restoring-force relationship that is not a straight line through the origin over the motion's range. Ideal SHM needs F ∝ -x.
Карта 339
Въпрос
At a horizontal ideal spring oscillator's turning points, how are kinetic and spring potential energy divided?
Отговор
Kinetic energy is zero and spring potential energy is maximum. The object momentarily stops at |x| = A.
Карта 340
Въпрос
For the same ideal spring with negligible damping and spring mass, which graph can determine k from measured periods and attached masses?
Отговор
Graph T² versus m. For T = 2π√(m/k), the slope is 4π²/k.
Карта 341
Въпрос
What makes a substance a fluid?
Отговор
It deforms continuously under a shear force and takes the shape of its container. Liquids and gases are fluids.
Карта 342
Въпрос
What is mass density?
Отговор
Mass per volume: ρ = m/V. Its SI unit is kg/m³.
Карта 343
Въпрос
For pressure that is uniform over a surface patch, how is it related to normal force and area?
Отговор
P = F_perpendicular/A. Pressure is a scalar field even though the contact force has direction.
Карта 344
Въпрос
What is volume flow rate?
Отговор
Volume passing a cross-section per time: Q = ΔV/Δt. Its SI unit is m³/s.
Карта 345
Въпрос
What is the buoyant-force magnitude on an object immersed in a static fluid whose density is uniform over the displaced volume?
Отговор
The weight of the displaced fluid: F_B = ρ_fluid gV_displaced. Here ρ_fluid is the uniform density over that volume.
Карта 346
Въпрос
What conditions support the basic Bernoulli model used here?
Отговор
Steady, incompressible, nonviscous flow along the compared flow path, with a completely filled pipe unless stated otherwise. Incompressible means a moving fluid element's density stays effectively constant. Pumps or major dissipative effects require extra terms.
Карта 347
Въпрос
Under the ideal model, how does average density predict whether a free object floats or sinks?
Отговор
It floats if its average density is less than the fluid's and sinks if it is greater. Equal average density gives neutral buoyancy when fully submerged; assume no support or other external force.
Карта 348
Въпрос
How are volume flow rate, cross-sectional area, and average fluid speed normal to that area related?
Отговор
Q = Av. This gives the volume crossing a completely filled pipe section per time.
Карта 349
Въпрос
How does a static fluid exert force on a surface?
Отговор
Many particle–surface interactions produce a net force perpendicular to the surface. A static fluid does not exert a tangential shear force.
Карта 350
Въпрос
How does pressure change with depth in a static uniform fluid?
Отговор
It increases by ΔP = ρgΔh. Greater depth means more fluid weight above each unit area.
Карта 351
Въпрос
What force balance holds for an object floating at rest when buoyancy and weight are its only vertical forces?
Отговор
F_B = mg. The object's weight equals the weight of the fluid it displaces.
Карта 352
Въпрос
What is the continuity equation for steady incompressible flow in one filled pipe?
Отговор
A₁v₁ = A₂v₂. The same volume flow rate passes each cross-section.
Карта 353
Въпрос
Why does a static fluid produce an upward buoyant force?
Отговор
Pressure is greater on the object's lower surfaces than on its upper surfaces. The vertical pressure forces do not cancel.
Карта 354
Въпрос
What is the absolute pressure at depth h below the open surface of a static, uniform liquid?
Отговор
P_abs = P_atm + ρgh. ρgh is the gauge pressure from the liquid column.
Карта 355
Въпрос
Immediately after a fully submerged object is released in a static, uniform ideal fluid, which way does it accelerate if its average density exceeds the fluid density and only weight and buoyancy act?
Отговор
Downward. Weight exceeds buoyant force, so the initial net force and acceleration point downward.
Карта 356
Въпрос
Water's average speed normal to a 0.020 m² pipe cross-section is 3 m/s. What is the volume flow rate?
Отговор
0.060 m³/s. Q = Av = 0.020×3.
Карта 357
Въпрос
What does the slope of a mass-versus-volume graph represent for one uniform material?
Отговор
Density. Since m = ρV, the line's slope is ρ.
Карта 358
Въпрос
How do gauge pressure and absolute pressure differ?
Отговор
Gauge pressure is measured relative to atmospheric pressure; absolute pressure is measured relative to vacuum. P_abs = P_atm + P_gauge.
Карта 359
Въпрос
For a fully submerged rigid object in a static, incompressible, uniform fluid, does buoyant force increase with depth?
Отговор
No. Displaced volume, fluid density, and g stay constant, so F_B stays constant despite higher absolute pressure.
Карта 360
Въпрос
For steady incompressible flow in a filled pipe, what happens to speed if cross-sectional area halves?
Отговор
It doubles. Continuity keeps Av constant.
Карта 361
Въпрос
When does a fluid element's velocity change?
Отговор
Its velocity changes when a nonzero net force acts on it. Pressure forces and gravity can contribute to that net force.
Карта 362
Въпрос
For steady, incompressible, nonviscous flow along the same flow path, what does Bernoulli's equation express?
Отговор
Conservation of mechanical energy per unit volume. Along that flow path, P + ½ρv² + ρgy stays constant under the stated conditions.
Карта 363
Въпрос
For a uniform object floating at rest in a uniform-density fluid with buoyancy and weight as its only vertical forces, what fraction of its volume is submerged?
Отговор
V_sub/V_object = ρ_object/ρ_fluid. A less-dense object floats with a smaller fraction submerged.
Карта 364
Въпрос
For steady incompressible flow in a filled pipe, what happens to speed if pipe radius halves?
Отговор
It becomes four times as large. Area is proportional to radius squared.
Карта 365
Въпрос
What does Pascal's principle say for a confined incompressible fluid at rest?
Отговор
An applied pressure change is transmitted throughout the fluid. The same pressure change acts at every connected point.
Карта 366
Въпрос
In a uniform static fluid, what does the slope of gauge pressure versus depth represent?
Отговор
ρg. For known g, the slope can determine fluid density.
Карта 367
Въпрос
Immediately after a fully submerged object is released in a static, uniform ideal fluid, which way does it accelerate if its average density is less than the fluid density and only weight and buoyancy act?
Отговор
Upward. Buoyant force exceeds weight, so the initial net force and acceleration point upward.
Карта 368
Въпрос
For steady incompressible flow in a filled pipe, area narrows from 0.040 m² to 0.010 m². If initial speed is 2 m/s, what is final speed?
Отговор
8 m/s. Continuity gives v₂ = A₁v₁/A₂.
Карта 369
Въпрос
What physical quantity does each term in P + ½ρv² + ρgy share?
Отговор
Energy per unit volume, equivalent to pressure. Every term uses units of pascals.
Карта 370
Въпрос
In one static fluid of uniform density, what experimental graph could test F_B = ρ_fluid gV_displaced?
Отговор
Graph measured buoyant force versus displaced volume. A line with slope near ρ_fluid g supports the model.
Карта 371
Въпрос
A uniform object of density 750 kg/m³ floats at rest in uniform-density water of density 1000 kg/m³, with buoyancy and weight as its only vertical forces. What fraction is submerged?
Отговор
0.75, or 75%. Use the density ratio for floating equilibrium.
Карта 372
Въпрос
A main pipe splits into two outlets during steady incompressible flow. What flow-rate relation holds?
Отговор
Incoming flow rate equals the sum of outgoing flow rates. Q_in = Q_out,1 + Q_out,2.
Карта 373
Въпрос
For steady, incompressible, nonviscous efflux with negligible losses, what is Torricelli's speed for an opening a vertical distance h below a large open surface?
Отговор
v = √(2gh). Both locations are open to atmospheric pressure, and the large surface makes the upper-fluid speed negligible.
Карта 374
Въпрос
Why does the same force create more pressure on a smaller area?
Отговор
Pressure is inversely proportional to area for fixed perpendicular force. Concentrating the force raises F/A.
Карта 375
Въпрос
A sample has mass 0.60 kg and volume 2.0×10⁻⁴ m³. What is its density?
Отговор
3.0×10³ kg/m³. Divide mass by volume.
Карта 376
Въпрос
What conservation law underlies the continuity equation for incompressible flow?
Отговор
Conservation of mass. Constant density turns equal mass flow into equal volume flow.
Карта 377
Въпрос
An immersed object rests on a scale that exerts an upward support force. If weight, buoyancy, and that support are its only vertical forces, with mg ≥ F_B, how is apparent weight related to buoyant force?
Отговор
N = mg - F_B. Here N is the upward scale-force magnitude. The fluid supports part of the object's weight, so the scale reading is no greater than its weight under the stated condition.
Карта 378
Въпрос
What is the SI unit of pressure?
Отговор
The pascal, Pa. One pascal equals 1 N/m².
Карта 379
Въпрос
How do pressures compare at the same horizontal level in one connected static fluid?
Отговор
They are equal. Container shape does not change pressure at a fixed elevation.
Карта 380
Въпрос
What does specific gravity compare?
Отговор
A substance's density with water's density. It is a dimensionless ratio, commonly ρ_substance/ρ_water.
Карта 381
Въпрос
How could collecting outflow test a volume flow rate predicted from area and average normal speed?
Отговор
Measure collected volume over a timed interval and compare ΔV/Δt with Av. Repeat trials and include volume and timing uncertainty.
Карта 382
Въпрос
How does the particle model distinguish a fluid from a rigid solid?
Отговор
Fluid particles can rearrange and flow past one another. A rigid solid resists sustained shape change.
Карта 383
Въпрос
At equal height along the same flow path in steady, incompressible, nonviscous flow, how are pressure and speed related?
Отговор
The faster region has lower static pressure. Along that flow path at equal height, P + ½ρv² remains constant.
Карта 384
Въпрос
A fully submerged object displaces 0.020 m³ of static water. Using ρ = 1000 kg/m³ and g = 10 m/s², what is F_B?
Отговор
200 N. F_B = ρgV = 1000×10×0.020.
Карта 385
Въпрос
Why can a steel ship float even though steel is denser than water?
Отговор
Its hollow shape makes the ship's overall average density less than water. It displaces enough water for buoyant force to balance weight.
Карта 386
Въпрос
How does an ideal hydraulic lift with a confined incompressible fluid at rest multiply force?
Отговор
Equal pressure change gives F₁/A₁ = F₂/A₂. The larger-area piston produces the larger force.
Карта 387
Въпрос
For steady, incompressible, nonviscous efflux with negligible losses, what graph can test Torricelli's relation while fluid head h varies?
Отговор
Graph v² versus h. With both locations open to atmospheric pressure and upper-surface speed negligible, the model predicts slope 2g.
Карта 388
Въпрос
What does incompressible mean in the introductory ideal-fluid model?
Отговор
A fluid element's density stays effectively constant as it moves. Its volume does not appreciably shrink under pressure changes.
Карта 389
Въпрос
At two points along the same flow path in steady, incompressible, nonviscous flow, how are pressure and height related when speed is equal?
Отговор
Pressure is lower at the higher point. P + ρgy remains constant.
Карта 390
Въпрос
How can water displacement measure an irregular solid's volume?
Отговор
Submerge it fully and measure the increase in displaced-water volume. The volume change equals the submerged solid's volume if no water enters it.
Карта 391
Въпрос
Two equal-volume samples have densities ρ and 3ρ. How do their masses compare?
Отговор
The denser sample has three times the mass. From m = ρV, mass scales with density at fixed volume.
Карта 392
Въпрос
How can scale readings in air and water determine buoyant force?
Отговор
Subtract the immersed scale reading from the air reading. When the object is at rest and air buoyancy is negligible, the decrease equals the liquid's buoyant force.
Карта 393
Въпрос
Static water has ρ = 1000 kg/m³. Using g = 10 m/s², what gauge pressure is 3 m below its open surface?
Отговор
30,000 Pa. P_gauge = ρgh = 1000×10×3.
Карта 394
Въпрос
During steady incompressible outflow, why can a large tank's top-surface speed be neglected compared with outlet speed?
Отговор
The tank's surface area is much larger than the outlet area. Continuity then makes the top-surface speed much smaller.
Карта 395
Въпрос
For a chosen fluid element in a horizontal region, what can a pressure difference do?
Отговор
It creates a net pressure force from higher pressure toward lower pressure and can accelerate the element by Newton's second law. Other forces must also be included when they matter.
Карта 396
Въпрос
How can buoyancy measurements in a static fluid of known uniform density determine an irregular object's volume?
Отговор
Measure buoyant force while the object is fully submerged, then use V = F_B/(ρ_fluid g). The fluid density must be uniform over the displaced volume.
Карта 397
Въпрос
A 200 N perpendicular force acts on area 0.040 m². What pressure does it create?
Отговор
5,000 Pa. P = F/A = 200/0.040.
Карта 398
Въпрос
Why doesn't a hydraulic lift multiply energy?
Отговор
The large-force piston moves a shorter distance. Ideally, input work equals output work.
Карта 399
Въпрос
A large open tank has steady, incompressible, nonviscous efflux with negligible losses. Using g = 10 m/s², what speed leaves an opening 5 m below the surface when upper-surface speed is negligible?
Отговор
10 m/s. Both locations are at atmospheric pressure, so v = √(2gh) = √100.
Карта 400
Въпрос
An object floats first in water and then in a denser liquid. How does its submerged fraction change?
Отговор
It decreases in the denser liquid. Less displaced volume is needed to provide the same buoyant force.

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